Geodesic
Asymptotics of the Gurevich--Pitaevskii universal special solution of the Korteweg--de Vries equation as~$|x|\to\infty$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 245-253

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A complete asymptotic expansion as $x\to\pm\infty$ of the Gurevich–Pitaevskii universal special solution of the Korteweg–de Vries equation $u_t+u_{xxx}+uu_x=0$ is constructed and validated. The expansion is infinitely differentiable in the variables $t$ and $x$ and, together with the asymptotic expansions of all its derivatives in independent variables, is uniform on any compact interval of variation of the time $t$.
Keywords: Korteweg–de Vries equation, nonlinear Schrödinger equation, asymptotic expansion.
Mots-clés : isomonodromy 
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     author = {B. I. Suleimanov},
     title = {Asymptotics of the {Gurevich--Pitaevskii} universal special solution of the {Korteweg--de} {Vries} equation as~$|x|\to\infty$},
     journal = {Trudy Instituta matematiki i mehaniki},
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B. I. Suleimanov. Asymptotics of the Gurevich--Pitaevskii universal special solution of the Korteweg--de Vries equation as~$|x|\to\infty$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 245-253. http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a23/